How can i merge one object smoothly into another while animating?
You may use shape keys to make such animation, but it demands joining the objects together.


Join the meshes with Ctrl+J. Connect the meshes' vertices in Edit Mode. Try to keep the topology clean. After making it one solid mesh add two additional edge loops (Ctrl+R) and place them as pictured below. These will be helpful for further creasing.


Go to Data header-->Shape Keys panel and add two shape keys being in Object Mode. Select the second one, press apply shapekeys in edit mode button and change its value to 1.000. Select the bottom of the character's neck in Edit Mode and press Shift+S-->Cursor to Selected (with a 3D cursor as a pivot point set). Use a border select tool (B) to select all the body vertices. Then press Ctrl+Num- to unselect the very top edge loop. Press S,0 to scale vertices. Slide the edge loops pictured above (press G twice) to crease the edge of a toilet. Your transformation animation is ready.


Now being in Object Mode apply the transformations to the object (Ctrl+A). Change the value of the shape key to 1.000 and keyframe it with I. Select the object and move it down (G,Z). Place it on the grid floor, then press I-->Location. Now go further on a timeline, press Alt+G to reset location, then keyframe the location again with I. Change the value of a shape key to 0.000 and keyframe it again.


Here's the .blend